My first comment on this, as I imagine would be everyone else's too:
What is the google login page all about on the opening page??
Clicking cancel (because hey, everyone expects a modicum of privacy, right?) just reloads the page. Bad practice in the extreme!

Edit - It's the same on the app version! I've never seen anything like it.
To be absolutely clear to anyone reading this, the UKPA does not endorse safarijigsaw in any of its forms as it stands.

There isn't any privacy issue. A sign-in via OAuth only lets me see your name and lets me authenticate you as you on my server via Google's servers. The OAuth sign-in method I employ is the most barebones method and only gets the minimum amount of user data as required by Google's systems: your name, and your Google Player ID. (as well as a way to authenticate)

A Google sign-in is required as it is the only way to securely store player data for a user's account. (like "gems" or save states)

Most Google Play jigsaw games, if they save user data at all, don't have a Google sign-in and rely on the device ID. That means if you get a new device, you are SOL. I have seen comments on various Google Play games where people pony up thousands of dollars only to have nothing saved on their actual account when they switch devices. Using the device ID is a good business model as 99% of people don't understand the implications of the Google sign-in, but bad practice in reality. So I either make you happy now and angry later, or angry now and never a customer.

Some jigsaw games use the Google Play Services save games state. That stores a limited amount of data and is hackable, so it's not good for storing (earned) gem counts.

An earlier version didn't have this requirement and many players unknowingly played a lower-quality game.